Equivalent Rectangular Stress Research Articles

Base joint hysteresis model for reinforced concrete assembly columns with post-pouring area

In response to the problem of uncontrollable grouting quality of traditional grouting sleeves in the connection between prefabricated components, a column base joint with post pouring area connected by grouting sleeves (PCGS) is proposed. Both the sleeve and post pouring area could cause differences in hysteresis characteristics between prefabricated and cast-in-place components. In order to investigate the hysteresis model of PCGS column base joint, the cyclic load tests and finite element parametric analysis of PCGS column base joint were conducted. The theoretical calculation method for load and displacement of PCGS column base joint at yield, peak, and ultimate characteristic points was established based on equivalent rectangular stress and plastic hinge length in joint area. The average ratios of theoretical calculations to test results for load and displacement at the above three characteristic points are 0.997, 0.983, and 0.983, and 1.020, 1.041, and 0.970, respectively, indicating that the theoretical calculation method can accurately predict the strength and deformation of PCGS column base joint. The dimensionless skeleton curve model with double broken lines in the elastic and strengthening stages, and exponential function in descending stage has been established based on the test and simulated results. The degradation behavior of unloading stiffness and bearing capacity was quantitatively described using the regression fitting method, and the hysteresis rule was defined. The established hysteresis model can effectively reflect the strength and stiffness degradation under cyclic loading, which can provide guidance for the elastic-plastic seismic response analysis of PCGS column base joint.

Effects of aspect ratios and strengthening methods on seismic behavior of masonry piers strengthened by using hybrid-fibers modified reactive powder concrete

Piers are the main load-bearing elements of masonry structures. Damage to piers in earthquakes will lead to the collapse of the whole structure, so piers need to be strengthened. In order to study the effectiveness of hybrid-fibers modified reactive powder concrete (HFMRPC) coating strengthening on masonry piers and the influence of different strengthening methods and aspect ratios on the seismic behavior of masonry structures, six masonry walls with different aspect ratios (0.8, 1.0, and 1.4) and strengthened by different methods (unreinforced, single-sided coverage in piers, double-sided coverage in piers, and double-sided cross-bracing) were tested under in-plane quasi-static loading. The test and analysis results showed that the seismic behavior of masonry walls in terms of bearing capacity, displacement ductility, stiffness, and energy dissipation was effectively enhanced by HFMRPC coating. The improvement range of ductility coefficient, initial stiffness, and cumulative energy dissipation were 86.3% ∼ 229.3%, 18.2% ∼ 104.0%, and 57.0% ∼ 139.7%, respectively. The most suitable strengthening method for strengthening piers was double-sided cross-bracing compared with other methods. The strengthening effect of the double-sided coverage in piers was improved with the increased aspect ratio. Additionally, masonry wall shear strength and flexural capacity calculation methods were proposed based on GB 50003-2011, N-M interaction diagrams, and equivalent rectangular stress block.

Analysis and calculation method for concrete-encased CFST columns under eccentric compression

This paper presents a computational method for concrete-encased concrete-filled steel tube (CFST) columns under eccentric compression, which adopts the form of equivalent rectangular stress integrated by material constitutive curve. When establishing finite element model via ABAQUS, confinement provided by stirrup was considered to modify the constitutive law of encased concrete, so that the numerical modeling was in good agreement with tests. By analyzing the simulation results, the applicability of basic assumptions, such as plane section assumption, was discussed, and a database of 207 models with various parameters was created. The developed method took into account the influences of geometric nonlinearities of section shape, and its accuracy was verified against various collected tests and the database. It turned out that the formula presented was applicable to a wide range and had sufficient precision, while the predictions of N-M interaction curves of concrete-encased CFST columns in EC4, AISC and CECS were conservative due to the ignorance of the exact integration about irregular section-shape.

A reassessment of the CSA S304 chi-factor for design of reinforced concrete masonry members: large-scale experimental investigation

An experimental investigation was conducted that consisted of 12 pairs of reinforced masonry specimens in which the two specimens were constructed with their longitudinal axes oriented parallel and perpendicular to the laboratory floor, respectively. This work was conducted to reassess the need for the χ-factor accounting for the direction of compressive stresses in masonry members in relation to the direction used to establish their masonry assemblage strength included in CSA S304-14— Design of Masonry Structures. Parameters investigated included block size and reinforcement ratio. Test results suggest that the χ-factor can be eliminated from future editions of CSA S304 but should be considered with caution: a review of the literature and the current tests show that, in some cases, voids may develop between the exterior webs of adjacent blocks and so may be the source of the reduction in the magnitude of the equivalent rectangular compressive stress block.

Analytical study and design approach of the axial and flexural response of reinforced masonry columns confined with FRP jackets

Using fiber-reinforced polymer (FRP) wraps has proven to be an effective and optimized confinement technique to upgrade the axial and flexural capacity of reinforced concrete (RC) and reinforced masonry (RM) columns. The axial capacity of FRP-confined masonry depends on both the compressive strength of masonry before strengthening and the confinement pressure provided by the FRP jacket. This study proposes a simplified methodology to design and analyze prismatic fully grouted reinforced masonry columns (RMCs) strengthened with FRP Jackets. The proposed design methodology included an analytical confinement model to predict the compressive strength gain in RMCs due to the effective confinement pressure provided by FRP jackets. The proposed procedure was also designed to predict the nominal capacity of RMCs for practical design applications, with columns subjected to both axial loading and bending moment. The essential parameters to perform detailed section analysis were established, and suggested expressions were proposed to obtain the parameter values. Practical values for the equivalent rectangular stress block parameters were proposed. The theoretical axial force-moment interaction diagrams obtained by the proposed procedure were compared with available experimental data. The experimental test results were in good agreement with the analytical predictions by a reasonable marginal error. Furthermore, the effect of five design variables on the axial-flexural interaction of FRP-wrapped RMCs was investigated. The variables considered in the parametric study were the number of FRP layers, radius of the corners, stiffness of the FRP composite, cross-sectional aspect ratio, and masonry compressive strength. The results showed that increasing the FRP layers, corner radius, and FRP jacket stiffness significantly enhanced the axial capacity of the FRP-confined RMCs. However, the increase in the masonry compressive strength and cross-sectional aspect ratio negatively affected the axial capacity gain ratio of FRP-strengthened RMCs.

Stress – Strain behavior of rubberized concrete under compressive and flexural stresses

Scrap tyres are among the most troublesome waste products in the world. Using recycled tyre rubber as a replacement of sand in concrete mixes is an approach to improve the ductility of concrete. The use of rubberized concrete has gained a lot of attention in the past decade to utilize the enhanced ductility in seismic resistance. The properties of the equivalent compressive stress block exposed to combined flexural and compressive stresses are used to design reinforced concrete components. The design parameters of the equivalent compressive stress block for rubberized concrete are not well established. This article presents an experimental investigation of the behavior of rubberized concrete, with the focus on identifying the stress block parameters. Two concrete groups were studied during this investigation with two different design strengths. Four different mixes were prepared for each group, with crumb rubber replacing fine aggregate by 0, 10%, 15%, and 20% of the volume. The mixes properties, such as slump, density, compressive strength, tensile strength, and stress-strain relationship were experimentally assessed and compared. The experimental investigation provided equivalent rectangular stress block characteristics as well as the final compressive strain for those members. The values were compared to those established in key design international codes.

The influence of coal gangue coarse aggregate on the mechanical properties of concrete columns

Using coal gangue as coarse aggregate is one of the solutions for the sustainable development of construction engineering. In this paper, the mechanical properties of coal gangue concrete (CGC) columns are investigated. The test results show that the failure modes of CGC columns under different replacement ratios are similar. In the loading process, the strain difference between CGC and reinforcement is small, indicating that there is sufficient bonding force between them. Coal gangue coarse aggregate can not effectively prevent the expansion of cracks, resulting in a decrease in the crack resistance of CGC columns. With the increase of coal gangue replacement ratio, the total deformation of the specimen increases, but the ductility decreases gradually. The reliability index of the bearing capacity limit state of CGC members should be improved in the design. Due to the large deformation of CGC, the stirrup is more important for the restraint of CGC column deformation, so increasing the stirrup ratio will be an effective method to improve the mechanical performance of CGC column. When calculating the bearing capacity of the CGC column, the parameters α and β of the equivalent rectangular stress block should be corrected according to the change of coal gangue replacement ratio.

In-plane lateral load transfer capacity of unreinforced masonry walls considering presence of openings

This study proposes mathematical models for the prediction of the in-plane lateral load capacity of unreinforced masonry (URM) walls considering potential failure modes and the presence of openings. The rocking strength is derived from the elasticity theorem for the compound stress condition under the assumption that rocking begins when the stresses at the extreme tensile fiber reach the tensile resistance capacity of the masonry. For toe crushing strength, the equivalent rectangular stress block specified in federal emergency management agency (FEMA) 273 is considered in the calculation of resultant compressive forces. The sliding and diagonal shear crack strengths are formulated based on the upper-bound theorem of concrete plasticity. The proposed models account for the effects of door or window openings on the failure mode and lateral load capacity of URM walls. The reliability of the proposed models is verified by comparing with test datasets comprising 202 URM walls without opening, 3 walls with door opening, and 4 walls with window opening. The proposed models confirm that URM walls are initially governed by the rocking rotation and subsequently ultimately fail via different mechanisms. It is also found that the empirical design equations specified in FEMA 273 and new zealand society for earthquake engineering (NZSEE) overestimate the rocking strength of URM walls and that their predicted their lateral load capacity significantly deviates from the test data. The proposed model results present comparatively better agreement with the test results. The mean and standard deviation of the ratios between the experimental and predicted results are 0.93 and 0.20, respectively, for URM walls without openings, and 0.92 and 0.14 respectively, for URM walls with openings. The proposed models rationally consider the effect of openings on the transition of the failure modes and the consequent reduction in the lateral load capacity.

Flexural Performance of FRP-Reinforced Geopolymer Concrete Beam

Fibre-reinforced polymer (FRP) rebar and geopolymer concrete (GPC) are relatively new construction materials that are now been increasingly used in the construction sectors. Both materials exhibit superior structural and durability properties that also make them a sustainable alternative solution. Due to the absence of any design standard for an FRP-reinforced GPC beam, it is important to validate the efficacy of available standards and literature related to other materials, e.g., FRP-reinforced conventional concrete or GPC alone. Four theories/design standards are considered for this comparison—ACI440.1R-15, CAN/CSA S806-12, parabolic stress block theory, and equivalent rectangular stress block theory for GPC under compression. The accuracy of these four approaches is also examined by studying the flexural performance of both the glass FRP (GFRP) and carbon FRP (CFRP). The FRP-reinforced beams are designed against the actual load they will be subjected to in a real-world scenario. It is concluded that parabolic stress block theory over-estimates the capacity, whereas CSA S806-12 yields the most accurate and conservative results. In addition, the flexural performance of the FRP-reinforced beams is evaluated in terms of ultimate, cracking, and service moment capacity, along with serviceable, ultimate, and residual deflection.

Analytical models for reverse arch and compressive arch action in horizontally restrained unbonded prestressed RC beam-column sub-assemblages

This paper presents the analytical models to predict the reverse arch action (RAA) and the compressive arch action (CAA) of unbonded prestressed reinforced concrete (UPRC) beam-column sub-assemblages under column removal scenarios. In the models, the realistic stress–strain model for concrete is applied to calculate the compression force sustained by concrete, instead of the equivalent rectangular concrete stress block. A linear variation of the strains for concrete and steel reinforcement along the beam length is assumed. Moreover, a notional eccentricity of eccentric force imposing on beam section is introduced in the RAA model to determine its bending moment. Comparisons between FEM’s and analytical results indicate that reasonable accuracy can be obtained in predicting not only the inverted camber and the RAA capacity of the sub-assemblages by the RAA model, but also the CAA capacity and the horizontal reaction force through the CAA model. Furthermore, the effects of effective prestress on the CAA of the sub-assemblages are investigated. Finally, through a contrastive analysis, it can be concluded that the increase of effective prestress is beneficial to the enhancement of CAA capacity to mitigate structural progressive collapse but worse to the ductility of beam section.

Equivalent stress block to characterise force–displacement behaviour of circular RC column considering steel bond slip

The compressive zone of concrete with a circular cross-section is simplified to an equivalent rectangular stress block with a width, height and thickness of the peak concrete strength considering the confinement ratio. The shape factors of the equivalent stress block at any concrete strain level are modelled through selected equations of the ratios of the axial load and moment sustained by compressive concrete. The proposed equivalent stress block is used to predict the force–displacement behaviour of a circular, reinforced-concrete (RC) column considering steel bond slip. A comparison with the test results of column specimens indicates that the proposed equivalent stress block can predict the lateral responses with good accuracy; moreover, the variation in the strain of longitudinal rebar and the deformation ratios of flexure and steel bond slip can also be reasonably predicted. The proposed equivalent stress block can be applied widely to other concrete models; furthermore, the capacity curve of the circular RC column can be reasonably predicted by the proposed simplified piecewise model based on the equivalent stress block.

Flexural design of precast, prestressed ultra-high-performance concrete members

Ultra-high-performance concrete (UHPC) is a special concrete mixture with outstanding mechanical and durability characteristics. It is a mixture of portland cement, supplementary cementitious materials, sand, and high-strength, high-aspect-ratio microfibers. In this paper, the authors propose flexural design guidelines for precast, prestressed concrete members made with concrete mixtures developed by precasters to meet minimum specific characteristics qualifying it to be called PCI-UHPC. Minimum specified cylinder strength is 10 ksi (69 MPa) at prestress release and 18 ksi (124 MPa) at the time the member is placed in service, typically 28 days. Minimum flexural cracking and tensile strengths of 1.5 and 2 ksi (10 and 14 MPa), respectively, according to ASTM C1609 testing specifications are required. In addition, strain-hardening and ductility requirements are specified. Tensile properties are shown to be more important for structural optimization than cylinder strength. Both building and bridge products are considered because the paper is focused on capacity rather than demand. Both service limit state and strength limit state are covered. When the contribution of fibers to capacity should be included and when they may be ignored is shown. It is further shown that the traditional equivalent rectangular stress block in compression can still be used to produce satisfactory results in prestressed concrete members. A spreadsheet workbook is offered online as a design tool. It is valid for multilayers of concrete of different strengths, rows of reinforcing bars of different grades, and prestressing strands. It produces moment-curvature diagrams and flexural capacity at ultimate strain. A fully worked-out example of a 250 ft (76.2 m) span decked I-beam of optimized shape is given.

Flexural capacity and ductility of lightweight concrete T‐beams

AbstractThe present study aims to estimate the flexural capacity and ductility of lightweight concrete T‐beams prepared using the expanded bottom ash and dredged soil granules (LWAC‐BS beams). Eight full‐scale beams were prepared under the main parameters including the unit weight and compressive strength of concrete and amount of longitudinal tensile reinforcement. The moment capacities and displacement ductility ratios measured for the present specimens were compared with those compiled from normal‐weight concrete (NWC) beams and lightweight concrete beams made using the expanded clay and fly ash granules (LWAC‐CF beams) with respect to the longitudinal reinforcement index (ωs). The coefficients for the equivalent rectangular stress block to assess the ultimate moment capacity of LWAC beams were formulated from the actual stress–strain curve of the concrete. The test results showed that the effect of the type of artificially expanded lightweight granules on the normalized cracking and ultimate moment capacities of LWAC beams was insignificant, whereas LWAC‐BS beams exhibited lower displacement ductility ratios than LWAC‐CF beams at the same ωs value. The maximum amount of longitudinal tensile reinforcement specified in ACI 318‐14 provision for preventing brittle failure of the beam needs to be lowered for LWAC beams. When determining the coefficients of the equivalent stress block for LWAC members, the concrete unit weight deserves consideration as a primary factor together with the compressive strength of the concrete.

Application of RC flexural theorems for member design under elevated temperature

Equivalent rectangular stress block is widely used for flexural design of reinforced concrete (RC) members. Conventionally, stress block parameters are obtained from extensive flexural tests of RC beams and columns. Parameters of the stress block are closely related to properties of concrete. Therefore, new stress block parameters are required when new materials, such as high-performance concrete, are used in construction, or materials face unusual scenarios such as higher temperature. Structural testing under elevated temperature is difficult and expensive, and hence, insufficient tests have been undertaken so far to derive the stress block parameters. This work produces stress block parameters for RC members under elevated temperature without doing experimental tests. By applying the newly developed RC flexural theorems, which were mathematically derived and applicable to general RC members, the relevant stress block parameters are obtained. This facilitates the flexural design of RC members under elevated temperature by engineers using the conventional stress block approach. The flexural behavior of RC members under elevated temperature is further studied, through parametric studies.

Analytical method for derivation of stress block parameters for flexural design of FRP reinforced concrete members

This work derives stress block parameters for fibre-reinforced polymer (FRP) reinforced concrete (RC) members by applying the newly developed RC flexural theorems without doing structural tests. The equivalent rectangular stress block method is widely used for flexural design of RC members. Conventionally, stress block parameters are obtained from extensive flexural tests of RC members. Parameters of the stress block are closely related to material properties. Therefore, new stress block parameters are required when new materials, such as FRP, are used in construction. Structural testing is expensive, and test data is often insufficient for derivation of stress block parameters when a new material is applied in practice. The derived stress block parameters from this work and relevant RC flexural strength are compared with experimental results as well as those recommended by ACI 440.1R-15 and CSA-S806-12. More accurate results are obtained using the proposed parameters compared with those calculated from existing design codes. The method can also result in significant savings in FRP material due to more accurate calculation. The proposed approach facilitates more accurate yet convenient design for flexural strength of FRP-reinforced concrete members by engineers using the conventional stress block approach.

THEORETICAL INVESTIGATION ON NORMAL SECTION FLEXURAL CAPACITY OF UHPC BEAMS

The relationships among peak compressive strain, cube compressive strength, elastic modulus, and axial compressive strength were established respectively based on 64 groups of Ultra High Performance Concrete (UHPC) compressive test data. The equivalent tensile strength of UHPC in the tensile zone was deduced through the mechanics of composite materials. Based on the plane section assumption, the formula for calculating normal-section flexural capacity of UHPC beams and the parameters of an equivalent rectangular stress block of UHPC in the compressive zone were deduced and the equivalent rectangular strength was calculated with the UHPC compressive constitutive relationship. Based on the data of 28 test beams, the feasibility of calculating the flexural capacity and the parameters of equivalent rectangular stress block was verified. The results show that the parameters of an equivalent rectangular stress block are reasonable and the calculated results of the normal-section flexural capacity of UHPC beams are in a good agreement with the experimental ones.

Experimental study on flexural behavior of ECC/RC composite beams with U-shaped ECC permanent formwork

To enhance the durability of a reinforced concrete structure, engineered cementitious composite (ECC), which exhibits high tensile ductility and good crack control ability, is considered a promising alternative to conventional concrete. However, broad application of ECC is hindered by its high cost. This paper presents a new means to address this issue by introducing a composite beam with a U-shaped ECC permanent formwork and infill concrete. The flexural performance of the ECC/RC composite beam has been investigated experimentally with eight specimens. According to the test results, the failure of a composite beam with a U-shaped ECC formwork is initiated by the crushing of compressive concrete rather than debonding, even if the surface between the ECC and the concrete is smooth as-finished. Under the same reinforcement configurations, ECC/RC composite beams exhibit increases in flexural performance in terms of ductility, load-carrying capacity, and damage tolerance compared with the counterpart ordinary RC beam. Furthermore, a theoretical model based on the strip method is proposed to predict the moment-curvature responses of ECC/RC composite beams, and a simplified method based on the equivalent rectangular stress distribution approach has also evolved. The theoretical results are found to be in good agreement with the test data.

Research on Concrete Columns Reinforced with New Developed High-Strength Steel under Eccentric Loading.

The use of new developed high-strength steel in concrete members can reduce steel bar congestion and construction costs. This research aims to study the behavior of concrete columns reinforced with new developed high-strength steel under eccentric loading. Ten reinforced concrete columns were fabricated and tested. The test variables were the transverse reinforcement amount and yield strength, eccentricity, and longitudinal reinforcement yield strength. The failure patterns were compression and tensile failure for columns subjected to small eccentricity and large eccentricity, respectively. The same level of post-peak deformability and ductility could only be obtained with a lower amount of transverse reinforcement when high-strength transverse reinforcements were used in columns subjected to small eccentricity. The high-strength longitudinal reinforcement improved the bearing capacity and post-peak deformability of the concrete columns. Furthermore, three different equivalent rectangular stress block (ERSB) parameters for predicting the bearing capacity of columns with high-strength steel are discussed based on test and simulated results. It is concluded that the China Code GB 50010-2010 overestimates the bearing capacity of columns with high-strength steel, whereas the bearing capacities computed using the America Code ACI 318-14 and Canada Code CSA A23.3-04 agree well with the test results.

Assessing Stress-Block Parameters in Designing Circular High-Strength Concrete Members Reinforced with FRP Bars

Several standards and guidelines allow the use of the equivalent rectangular stress block (ERSB) as a simple concept to accurately predict flexural strength with or without axial force. North American codes (ACI 318 and CSA A23.3) allow the use of the ERSB as an alternate approach to stress-strain relationships in predicting the strength of high-strength concrete (HSC) reinforced with steel bars (steel-HSC-RC). The strength of high-strength concrete specimens reinforced with fiber-reinforced polymer (FRP) bars (HSC-FRP-RC) could be predicted similarly to steel-RC specimens. This research represents an early attempt to investigate the applicability of several ERSBs proposed by different associations to predict the strength of HSC-FRP-RC specimens subjected to combined flexural and compression loads. An experimental database was assembled from 92 specimens studied by the authors and others. The test parameters included concrete strength, level of eccentricity, reinforcement type, glass fiber–reinforced polymer (GFRP) reinforcement ratio, and confinement configuration. Extensive analyses were integrated into the test results to investigate the impact of each test parameter on ERSB parameters. The accuracy and conservativeness of several models were assessed. Comparing the predictions for the tested FRP-RC specimens made with normal-strength concrete (NSC) and HSC revealed that the level of conservatism dramatically decreased for all models, leading to overestimations for some specimens. The American Concrete Institute model always had the lowest level of conservatism, which led to overestimations of some specimens for steel and FRP-RC specimens made with HSC among all the other models. Modified expressions of the ERSB given in ACI 440.1R and CSA S806 were developed. The results indicate good and safe correlation of predicted and measured strength values with reasonable levels of conservatism.

Stress-strain response of high-volume fly ash self-compacting concrete (HVFA-SCC) under uniaxial loading and its effect on the reinforced HVFA-SCC nominal strength

Utilization of High-Volume Fly Ash-Self Compacting Concrete (HVFA-SCC) as a reinforced concrete structural element requires a rational analysis to accommodate the mechanical characteristics of HVFASCC. This study aims to investigate and analyze the mechanical characteristics of HVFA-SCC by examining the experimentally obtained complete stress-strain behavior of this concrete. The results indicate that the compression stress-strain curve of HVFA-SCC is diverse to that of normal concrete (NC) in which the average area under the curve represents 64% to that of NC. Consequently, the equivalent rectangular compression stress for calculating the nominal flexural strength of reinforced HVFASCC section should be modified by a factor of 0.64. Based on this theoretical analysis, a close agreement exists between the predicted nominal flexural strength and the experimental result.